Question

The Summer Theatre charges $4 per ticket, and it sells an average of 400 tickets nightly. The manager estimates that the ticket sales would decrease by 50 for each $1 increase in the ticket cost. What is the most profitable price to charge?

Answer 1

profit = revenue-cost
If there are x price increases,
revenue=(4+x)(400-50x)
actually, you don't mention cost, but that doesn't matter, since it will not change with the price.
So, to get maximum revenue, just find the vertex of

y=(4+x)(400-50x)=1600+200x-50x^2
it will occur at x = -b/2a = 2
so, the price will be 4+2= $6